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Chapter 6 Capital Structure and Moral Hazard

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					Chapter 6: Capital Structure and Moral Hazard


               Albert Banal-Estanol


                  October 2008
Chapter 6                                   2                             Albert Banal-Estanol



                          Credit Rationing Puzzle
   • Why are lenders not willing to raise interest rates if the demand for loans exceeds
     their supply at the prevailing rates?
   • Why loan markets are personalised?
   • Explanation: asymmetric information between borrowers and lenders
   • Problems of moral hazard (this lecture) and adverse selection (next lecture)
   • In both cases higher interest rates reduces the stake of the borrower
   • Reduced stake may demotivate the borrower and may lower the probability of
     repayment (moral hazard)
   • If lenders cannot distinguish good from bad borrowers, higher interest rates may
     attract worse borrowers (adverse selection)
Chapter 6                                  3                          Albert Banal-Estanol



                 A Simple Model of Credit Rationing
   • Agent has a project that requires investment I but has assets A < I
     (needs to borrow I − A)

   • Project may be successful (probability p) and yield R > 0
     or fail (probability 1 − p) and yield 0

   • Agent may exert effort (p = pH ) or shirk (p = pL), with ∆p = pH − pL > 0

   • If she shirks she obtains private benefits B > 0

   • Both borrower and potential investors are risk neutral

   • Borrower has limited liability (no punishment for failure)

   • Lenders are competitive (make zero profit)
Chapter 6                                4                            Albert Banal-Estanol



                               Loan Contract
   • A loan contract specifies how the profit is shared between lenders and borrower:
     Both should get 0 in case of failure (limited liability)
     In case of success, sharing rule Rb + Rl = R

   • Competitive lending implies (assuming effort is exerted): pH Rl = I − A

   • The rate of interest is given by (1 + i)(I − A) = Rl or 1 + i = 1/pH

   • Hence, unless pH = 1, we have i > 0 (default premium)

   • Assume that project has positive NPV if the manager exerts effort, pH R−I > 0

   • But negative NPV if not, pLR − I + B < 0 (even adding B)

   • Hence, rewriting, pLRl − (I − A) + pLRb + B − A < 0 (effort is necessary)
Chapter 6                                5                  Albert Banal-Estanol



                             Summary: Timing
  1. Loan agreement (sharing rule in the case of success)

  2. Investment

  3. Moral hazard (effort or shirk?)

  4. Outcome (and payments)
Chapter 6                                   6                           Albert Banal-Estanol



                                Credit Analysis
   • Need to ensure that borrower exerts effort
   • Borrower’s trade-off: private benefits vs. higher probability of success
   • Incentive compatibility constraint:
                                   pH Rb ≥ pLRb + B
      or
                                                B
                                           Rb ≥
                                                ∆p
   • This is the minimum the agent must keep
   • Maximum that can be pledged (promised to the bank) is
                                                B
                                   R − Rb = R −
                                                ∆p
Chapter 6                                   7                             Albert Banal-Estanol



   • Since this is paid only in the case of success, agent is financed only if
                                     Ã              !
                                               B
                                   pH R −               ≥I −A
                                               ∆p
      or
                               Ã           !
                                      B                 B
                 A ≥ I − pH R −                 = pH       − (pH R − I) = A
                                      ∆p                ∆p
   • To make things interesting assume that A > 0 or
                                       B
                                    pH    > pH R − I
                                       ∆p

      i.e. the NPV is smaller than the necessary rent
   • Thus financing is possible only when A ≥ A, even if, when A < A, the project
     also has positive NPV (credit rationing)
Chapter 6                                  8                             Albert Banal-Estanol



   • Lenders may not grant a loan even if borrower is willing to give a high fraction
     of the return

   • The borrower needs to have enough assets to be financed (A ≥ A)

   • In this case, borrower’s stake is given by
                                        I −A     I −A   B
                       R − Rl = R −          ≥R−      =
                                          pH       pH   ∆p
   • Borrowers’ net payoff (subtracting A) is given by
              (
                  0                                                if A < A
                  pH Rb − A = pH (R − Rl ) − A = pH R − I         if A ≥ A

   • Borrower receives entire surplus if project is funded (lender breaks even)
Chapter 6                                9                            Albert Banal-Estanol



                                  Conclusions
   • Because of moral hazard there is a limit to pledgeable income

   • There is credit rationing and projects with positive NPV may not be funded

   • The borrower needs to have enough assets to be financed

   • Higher private benefits, higher threshold for financing

				
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